anonymous
  • anonymous
I don't really get this. Question: Use the rules for exponents and roots to prove that 512^2/3 = 16^3/2
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
Do you mean a rigorous formal proof?
anonymous
  • anonymous
I don't really know. This is what the question was and I don't get it.
anonymous
  • anonymous
Do you understand how to use logarithms?

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anonymous
  • anonymous
No
anonymous
  • anonymous
Ah, you will want to understand natural logarithms for this question, I can explain it.
anonymous
  • anonymous
\[y = \log_b x\] \[x = b^y\]
anonymous
  • anonymous
If we take the natural logarithm of \[512^{\frac{2}{3}}\] \[\frac{2}{3}\ln(512)\]
anonymous
  • anonymous
We can pull the exponent out
anonymous
  • anonymous
So, is that a cube root? That we ended up with?
precal
  • precal
|dw:1360950294527:dw|
precal
  • precal
|dw:1360950347726:dw|
precal
  • precal
|dw:1360950360574:dw|
precal
  • precal
|dw:1360950390774:dw|
precal
  • precal
|dw:1360950432326:dw|
precal
  • precal
yes they are both equivalent
anonymous
  • anonymous
Thanks, so much. That makes sense now.
precal
  • precal
yw
precal
  • precal
no need to use logs here
anonymous
  • anonymous
just using exponents :512=2^9 so 512^(2/3)=2^6 and 16^(3/2)=2^6 so both are equal
anonymous
  • anonymous
Thanks
precal
  • precal
yw

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